Scalar Casimir effect for a<i>D</i>-dimensional sphere

Abstract

The Casimir stress on a D-dimensional sphere (the stress on a sphere is equal to the Casimir force per unit area multiplied by the area of the sphere) due to the confinement of a massless scalar field is computed as a function of D, where D is a continuous variable that ranges from -\ensuremath{\infty} to \ensuremath{\infty}. The dependence of the stress on the dimension is obtained using a simple and straightforward Green's function technique. We find that the Casimir stress vanishes as D\ensuremath{\rightarrow}+\ensuremath{\infty} (D is a noneven integer) and also vanishes when D is a negative even integer. The stress has simple poles at positive even integer values of D.